Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper.
In a large bowl stir together the flour, baking soda, and salt.
In a large bowl using a hand mixer, or using a stand mixer, cream together the butter and sugar. Keep mixing and add in the vanilla and vinegar.
Slowly add the flour, baking soda, and salt mixture, a little at a time, into the mixing bowl with the wet ingredients. Slowly mix together until just combined.
If the batter is too dry, add a tablespoon of milk and stir. If more is needed, add another half tablespoon at a time until you have the right consistency. You don't want the dough to be too wet or sticky, and you don't want it to be too dry. If it is too wet or sticky, you can add a couple of tablespoons of flour to try to get the right consistency.
If you need to firm up the dough, you can refrigerate it for an hour or two. For the batch of cookies in the photograph, I did not refrigerate the dough as it has the correct consistency.
Bake the cookies in a preheated 375 degree oven from 8 - 12 minutes, or until the cookies are lightly golden brown on the edges. (I give a range since ovens heat differently. I recommend checking the cookies after 8 minutes and, if they are not ready, keeping an eye on them until they are done.)
Let the cookies cool on the cookie sheet for about 2 to 3 minutes. Then transfer the cookies to a wire rack and let the cookies cool down for about 10 minutes. Once the cookies are completely cooled, either serve or store in an air-tight container.